Diffractive optical elements (DOE's) are well known and fulfill important roles in industrial and military applications, in imaging, in medicine, in the storage, processing and transmission of information, and elsewhere. Digital DOE's, have been described by B. R. Brown and A. W. Lohmann in the article “Complex Spatial Filtering with Binary Masks”, published in Applied Optics, Vol. 5, p. 967ff, (1966). Such digital DOE's have generally been produced by means of mechanical micro-engraving, electron beam, ion beam or chemical etching, electron lithography or photolithography, or by other suitable techniques.
The mathematical functionality of a DOE can be expressed in terms of the field R({right arrow over (r)}) produced after imaging by the DOE of an incident light field S({right arrow over (u)}). This image field is given by equation 1:                               R          ⁡                      (                          r              _                        )                          =                              ∫            D                    ⁢                                    S              ⁡                              (                                  u                  _                                )                                      ⁢                          T              ⁡                              (                                  u                  _                                )                                      ⁢                                          exp                ⁡                                  (                                      ik                    ⁢                                          ⅆ                                              (                                                                              r                            _                                                    ,                                                      u                            _                                                                          )                                                                              )                                            /                              ⅆ                                  (                                                            r                      _                                        ,                                          u                      _                                                        )                                                      ⁢                          ⅆ              s                                                          (        1        )            where S({right arrow over (u)}) is the incident light field at the surface, s, of the DOE,                T({right arrow over (u)}) is the complex transmission coefficient of the DOE,        d({right arrow over (r)}, {right arrow over (i)}) is the optical path from point {right arrow over (r)} to {right arrow over (u)} in the imaging space, and   ∫  D        is the integral over the surface, s, of the DOE.        
Equation (1) is the Kirchhoff approximation for the solution of the scalar Dirichlet problem with infinite boundary conditions, and with Sommerfeld radiation conditions. Equation (1) can alternatively be interpreted as the Fresnel transformation of the field S({right arrow over (u)})T({right arrow over (u)}) from the surface of the DOE to the point {right arrow over (r)}.
In order to construct the desired DOE, the inverse problem has to be solved, whereby the incident field S({right arrow over (u)}) and the transmitted field R({right arrow over (u)}) are known and the appropriate complex transmission function of the DOE-T({right arrow over (u)}), has to be calculated. Such a DOE then produces the desired transformation of the incident field such that the correct field is formed in the image plane. The method of representing the DOE by means of a function T({right arrow over (u)})is performed by assigning complex values of the transmission function to discrete pixels of the DOE. The number of pixels chosen depends on the size of the DOE and its resolution. The values of the transmission function for each pixel can be calculated by means of scalar diffraction theory, and form a Fourier transform of the model field. Evaluation of this Fourier series requires some approximations. Several numerical methods and procedures for the calculation of DOE's, both direct and indirect, have been proposed in the prior art. Examples of such methods are given, for instance by D. Brown and A. Kathman, in the article “Multi-element diffractive optical designs using evolutionary programming” published in SPIE Vol. 2404, p.17ff, 1995; by J. N. Mait, in “Review of multi-phase Fourier grating design for array generation”, published in SPIE Vol. 1211, p. 67ff, 1990; by V. A. Soifer, et al., in “Multifocal diffractive elements”, published in Optical Engineering, Vol. 33, p. 3610ff, November 1994; and by N. L. Kazansky and V. V. Kotlyar, in “Computer-aided design of diffractive optical elements”, published in Optical Engineering, Vol. 33, p. 3156ff, (October 1994). These different methods are intended for different types of DOE and field transformations. A review of the problems associated with these methods, and various discretization quantization and errors are discussed in “Some effects of Fourier domain phase quantization” by J. W. Goodman and A. M. Silvestri, published in IBM Journal of Research and Development, Vol. 14, p. 478ff, (1970) and in “Aliasing errors in digital holography” by J. Buklew and N. C. Galaher, published in Journal of Applied Optics Vol. 15, p. 2183ff, (1976).
A major drawback of the prior art conventional methods of producing computer-generated DOE's is that they are principally two dimensional in nature and are located on the surface of the DOE. Such DOE's have found limited use because of the complexity of constructing integrated multi-element devices from an assembly of 2-dimensional devices. The need to maintain correct alignment of a number of separate elements, also reduces the reliability of such a device. A further serious limitation is the inability to produce a coherent arrangement of independent sequential devices and a 3-dimensional spatial diffractive structure. These problems are analogous to the differences found in the prior art between conventional 2-D Gabor holograms and 3-D Lipman-Denisyuk holograms, as described by Denisyuk in the article “Optical Properties of an Object as Mirrored in the Wave Field of its Scattered Radiation”, published in Optics and Spectroscopy, Vol. 15, pp. 522-532, (1963). This difference is analyzed by Van Heerden in the article “Theory of optical information storage in solids”, published in Applied Optics, Vol. 2, pp.764ff, (1963).
A number of different types of DOE's, produced according to prior art methods and apparatus, are described in the following documents: U.S. Pat. No. 5,291,317, to Newswanger et al, describes methods and apparatus for creating a plurality of holographic diffraction grating patterns in a raster scan fashion; U.S. Pat. No. 3,905,674, to Ruell et al, describes apparatus for producing one-dimensional holograms; U.S. Pat. No. 4,140,362, to Tien et al, describes a method for forming focusing diffraction gratings by production of a predetermined interference pattern on photosensitive film; U.S. Pat. No. 4,516,833, to R. L. Fusek describes the production of high performance optical spatial filters; U.S. Pat. No. 4,846,552, to W. B. Veldkamp et al, describes a method of fabricating high efficiency binary planar optical elements based on photolithographic techniques; U.S. Pat. No. 5,428,479, to R. A. Lee describes a method of manufacture of a diffraction grating with assembled point gratings; and U.S. Pat. No. 5,818,988 to R. A. Modavis describes a method of forming a grating in an optical waveguide utilizing photosensitive materials. All of the above-cited prior art methods have one or more of the disadvantages mentioned in the previous paragraph.
Furthermore, in U.S. Pat. No. 5,761,111 to E. N. Glezer, are described methods of providing 2- or 3 dimensional optical information storage in transparent materials by controllably focusing ultra-short laser pulses into a transparent medium. Volume DOE's are mentioned therein as one of the applications for the method. However, no details are provided, nor are any methods suggested of how to calculate the necessary “information” for storage in the transparent medium to produce such a DOE.
There therefore exists a serious need for a method of constructing intravolume multi-element DOE's, which overcome disadvantages of prior art DOE's.
All of the documents mentioned in this section, and in the other sections of this specification, are hereby incorporated by reference, each in its entirety.